First slide

Properties of ITF

Question

If $\tan^{- 1} x + 2 \cot^{- 1} x = \frac{2 π}{3}, then x =$

Moderate

A

3
B

$\sqrt{3}$
C

$\sqrt{2}$
D

$\frac{\sqrt{3} - 1}{\sqrt{3} + 1}$

Solution

We have,
$\begin{array}{l} \tan^{- 1} x + 2 \cot^{- 1} x = \frac{2 π}{3} \\ \Rightarrow \tan^{- 1} x + 2 (\frac{π}{2} - \tan^{- 1} x) = \frac{2 π}{3} \Rightarrow \tan^{- 1} x = \frac{π}{3} \Rightarrow x = \sqrt{3} \end{array}$

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